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Probability Calculator

Calculate probability using explicit client-side inputs.

Probability Calculator Inputs

Results computed instantly — your data never leaves your device.

Live Probability Calculator Results

Real-Time

Exact probability

4.3945%

Binomial probability for exactly k successes.

100% Client-SidePrivate & Secure

How to Use the Probability Calculator

  1. 1

    Enter the number of successful outcomes k.

  2. 2

    Enter the total number of trials n.

  3. 3

    Enter the success probability as a percent.

  4. 4

    Review the exact probability for k successes.

Formula & Mathematical Basis

P(X=k) = C(n,k)p^k(1−p)^(n−k).

Variable Key

n

Total number of independent trials

k

Exact number of successes

p

Success probability as a decimal

📝 The interface accepts p as a percentage and guards cases where k is outside 0 through n.

Step-by-Step Examples

1

Exactly two successes

Scenario: Use k = 2, n = 4, and p = 50%.

  1. 1.Convert 50% to p = 0.5.
  2. 2.Count combinations: C(4,2) = 6.
  3. 3.Multiply 6 × 0.5² × 0.5².
  4. 4.Obtain 0.375, or 37.5%.
✅ The probability of exactly two successes is 37.5%.

Practical Use Cases

  • Teach binomial probability.
  • Estimate an exact outcome count in repeated independent trials.
  • Compare probabilities under different success rates.

Common Pitfalls

  • Confusing exactly k with at least k.
  • Entering a percentage as a decimal percentage twice.
  • Using the model when trials are dependent.

Frequently Asked Questions

Does this calculate at least k successes?

No. It calculates exactly k successes for the inputs shown.

What if k is greater than n?

The guarded result is zero because that outcome is impossible.

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